2012 Fiscal Year Final Research Report
Research on combinatorics over Galois rings
| Project/Area Number |
20540014
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kanazawa University |
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Principal Investigator |
YAMADA Mieko 金沢大学, 数物科学系, 教授 (70130226)
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| Project Period (FY) |
2008 – 2012
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| Keywords | ガロア環 / 差集合 / 符号理論 / ガウス和 / designs / Hadamard行列 |
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| Research Abstract |
We constructed infinite families of difference sets over Galois rings of characteristic an even power of 2. The difference set over a Galois ring of characteristic 2^n is embedded in the ideal part of the difference set over a Galois ring of characteristic 2^n+2 . We introduced a new operation in a Galois ring and the Gauss sums associated with the character under this new operation play an important role of the proof. Furthermore, we proved there exist Reed-Muller codes with embedding system and showed several properties of them.
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